Contribution and Reservation

(73·10²¹⁰-1)/9 =: 8(1)₂₁₀_<211>; = 4357 · 6105623 · 12874391 · 11467321500049_<14> · 159146701132862403468910433_<27> · 367493736339136226915303269_<27> · [35312343521712681618695493375872053156061942867895018095094168912653652760761342064849100029226373575195953805408158436534796607_<128>] SUBMIT/RESERVE

Status

Expression:	(73·10²¹⁰-1)/9
Composite Factor:	353123435217126816186954933758720531560619428678950180950941 689126536527607613420648491000292263735751959538054081584365 34796607 (128-digit)
Status:	Not factored. Not reserved. You can submit its factors or reserve it for submitting in the future.

How to factor it

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 211.86-digit and the GNFS difficulty is 127.55-digit. GNFS must be faster than SNFS. It will take about 5 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 81111_210.
Put the following polynomial file 81111_210.poly in there too.
And then, run "perl factMsieve.pl 81111_210".

81111_210.poly ^*1

# Murphy_E = 1.015878e-10, selected by Jeff Gilchrist
n: 35312343521712681618695493375872053156061942867895018095094168912653652760761342064849100029226373575195953805408158436534796607
Y0: -4098367390715557634176686
Y1: 107671652622611
c0: -15582621154640285595018632905645
c1: 1364929613925853108227937943
c2: -2138983072736863525007
c3: -22987644356521067
c4: 8221250868
c5: 30540
skew: 426252.16
type: gnfs
# selected mechanically
rlim: 8400000
alim: 8400000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 128-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
40	3e6	2318	Wataru Sakai	Jun 1, 2009
40	3e6	2318 / 503
45	11e6	407	Dmitry Domanov	Jun 2, 2009
		407 / 3812
		/ 3405
50	43e6	43	Dmitry Domanov	Jun 2, 2009
		43 / 7374 (1014)
		/ 7331 (971)
55	11e7	0 / 17710 (3041)
55	11e7	/ 17710 (3041)
60	26e7	0 / 42003 (7618)
60	26e7	/ 42003 (7618)

Command line to find prime factors up to about 45-digit

echo 35312343521712681618695493375872053156061942867895018095094168912653652760761342064849100029226373575195953805408158436534796607 | ecm -n -c 3405 11e6

Command line to find prime factors up to about 50-digit

echo 35312343521712681618695493375872053156061942867895018095094168912653652760761342064849100029226373575195953805408158436534796607 | ecm -n -c 7331 43e6

Command line to find prime factors up to about 55-digit

echo 35312343521712681618695493375872053156061942867895018095094168912653652760761342064849100029226373575195953805408158436534796607 | ecm -n -c 17710 11e7

Command line to find prime factors up to about 60-digit

echo 35312343521712681618695493375872053156061942867895018095094168912653652760761342064849100029226373575195953805408158436534796607 | ecm -n -c 42003 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation